London (AFP) - Britons are reluctant to get too involved in tackling Islamic State jihadists, a new poll showed on Monday, despite Prime Minister David Cameron's call for a "firm security response".

Cameron on Sunday said the brutal extremist group, which has overrun swathes of northern Iraq and Syria, could threaten Britain and should be confronted as part of a "generational struggle against a poisonous and extremist ideology".

Yet only a fifth of Britons feel their country should seek to defeat the group in its entirety and 30 percent think Britain should not get involved "and leave the situation to run its course".

Cameron has struggled to muster support for military action in the Middle East given the country's strained finances and public wariness after the 2003 Iraq invasion, now widely seen as an ill-conceived and expensive failure.

A further 29 percent of respondents thought Britain should try to stop Islamic State making any further gains in Iraq, Syria or elsewhere, but not completely eradicate the group.

Pollster Comres surveyed 2,042 adults on behalf of ITV News over the weekend, when US-backed Kurdish and state forces recaptured Mosul dam, Iraq's largest, from Islamic State fighters.

The survey also showed that only 24 percent of people think the government should allow Iraq's Christians at risk of persecution to resettle in Britain, and even fewer think Iraqi Muslims at risk of persecution should be allowed in.

Respondents were evenly split on whether to arm Kurdish peshmerga forces fighting Islamic State, although almost half agreed with Iraq's former foreign minister Hoshyar Zebari that given the 2003 invasion Britain and the US have a "moral responsibility" to save Iraq from collapse.

Britain is stepping up its role in Iraq beyond a humanitarian mission and the involvement is set to last months, Defence Minister Michael Fallon said in comments published Monday, without giving details.

British aircraft have been on reconnaissance missions over the north of the country, but Cameron on Sunday said "sending armies to fight or occupy" should be avoided.